De-identification has its limits and information can still be learned even from anonymized datasets. An alternative to this is something like Sharemind [1][2] where sound cryptography is used to make secure multi-party computation possible.
I'm not sure what measures Mimic takes (beyond just stripping demographic info), but a given patient's pattern of healthcare interactions make quite a unique fingerprint -- and some parts of that fingerprint are likely public information for some patients.
E.g., imagine a celebrity who (you can find from the tabloids) was treated at X hospital for a sprained ankle on 2012-07-14, and gave birth to a daughter at Hospital Y on 2014-04-01. If her record -- completely "anonymized" -- is in a data set that lets you search for patients matching these two events... it seems fairly likely you'd be able to narrow it down to only a few candidates, or quite likely an exact match. And then once you have her pseudonym/ID, does the rest of the record reveal anything interesting? An abortion no one knew about (possibly not even her partner)? A venereal disease treatment?
Even the fact that a patient had an appointment at a given clinic is sensitive data -- e.g., seeing an IVF specialist, or oncologist, etc..
It's a tricky field to navigate.